Chin up! I'm kinda with Arizoni on this. If your right leg's not suddenly getting a warm wet feeling on the road, I'd just carry on and sort that dribble out later...maybe. For now, just grab
a 50 pack of these rags and ride on, baby! A lightly oily rag is just what that bike needs now for overall "soothing" and purging of those oxides. Just roll one up and tie it up in a knot on the handlebar: handy and looks kinda romantic--like a big greasy rose.
It's altogether possible that if you resist messing with that stud anymore, and it's now just a mild weeping on these rather hot days we've been having, that enough oil might eventually bake up in those micro-crevasses to really help stanch that drooling. It's a pretty common outcome for minor oil dribblages around the head and cylinder barrel. They often enough just kind of "clot" and sort themselves out. For example, my old Norton would start weeping somewhere between the head and cylinder on those longer 300+ mile summertime trips, and then quickly calm down again once back to its humdrum daily driver routine. I presume those sustained exertions of the wide open roads kind of flushed the useful cloggery, which then restored itself during less iron butted jaunts.